Numerically Analyzing Phase Transition of the Strong Nuclear Force
Faculty Mentor Name
Kieran Holland
Research or Creativity Area
Natural Sciences
Abstract
We numerically analyze Polyakov loop configurations generated by running Monte Carlo simulations on a fine hypercubic lattice. Our main objective is to numerically approximate the critical temperature of the gluon phase transition by taking the continuum limit as the lattice spacing goes to zero and the spatial box size approaches infinity. To achieve this, we extract the critical coupling from the Polyakov loop data by computing the ratio of spins in and outside three chosen Z(3) triangles, plotting this ratio as a function of the bare coupling, and estimating the critical coupling as the point where the ratio crosses zero.
We validate this geometric approach against the critical coupling derived as the peak of the Polyakov loop susceptibility. Throughout the analysis, we used bootstrap resampling to estimate uncertainties and the Akaike information criterion to determine the best-fitting models. Ultimately, as we increase the box size, we observe convergence of the critical couplings obtained from both susceptibility and geometric methods. This convergence provides the foundation for estimating the critical temperature at which the phase transition of the strong nuclear force occurs.
Numerically Analyzing Phase Transition of the Strong Nuclear Force
We numerically analyze Polyakov loop configurations generated by running Monte Carlo simulations on a fine hypercubic lattice. Our main objective is to numerically approximate the critical temperature of the gluon phase transition by taking the continuum limit as the lattice spacing goes to zero and the spatial box size approaches infinity. To achieve this, we extract the critical coupling from the Polyakov loop data by computing the ratio of spins in and outside three chosen Z(3) triangles, plotting this ratio as a function of the bare coupling, and estimating the critical coupling as the point where the ratio crosses zero.
We validate this geometric approach against the critical coupling derived as the peak of the Polyakov loop susceptibility. Throughout the analysis, we used bootstrap resampling to estimate uncertainties and the Akaike information criterion to determine the best-fitting models. Ultimately, as we increase the box size, we observe convergence of the critical couplings obtained from both susceptibility and geometric methods. This convergence provides the foundation for estimating the critical temperature at which the phase transition of the strong nuclear force occurs.
